Physical security with power beacon assisted in half-duplex relaying networks over Rayleigh fading channel: performance analysis

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ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018

DOI: 10.12928/TELKOMNIKA.v18i2.15857  1072

Physical security with power beacon assisted in half-duplex relaying networks

over Rayleigh fading channel: performance analysis

Phu Tran Tin¹, Duy-Hung Ha², Luu Gia Thien³, Tran Thanh Trang⁴

1Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Vietnam

2Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Vietnam

3Posts and Telecommunications Institute of Technology Ho Chi Minh City Campus, Vietnam

4National Key Laboratory of Digital Control and System Engineering, Vietnam

Article Info ABSTRACT

Article history:

Received Jul 24, 2019 Revised Nov 19, 2019 Accepted Dec 4, 2019

In this research, we proposed and investigated physical security with power beacon assisted in half-duplex relaying networks over a Rayleigh fading channel. In this model, the source (S) node communicates with the destination (D) node via the helping of the intermediate relay (R) node.

The D and R nodes harvest energy from the power beacon (PB) node in the presence of a passive eavesdropper (E) node. Then we derived the integral form of the system outage probability (OP) and closed form of the intercept probability (IP). The correctness of the analytical of the OP and IP is verified by the Monte Carlo simulation. The influence of the main system parameters on the OP and IP also is investigated. The research results indicated that the analytical results are the same as the simulation ones.

Keywords:

Energy harvesting (EH) Half-duplex (HD) Intercept probability (SP) Monte carlo simulation

Relaying network This is an open access article under the CC BY-SA license.

Corresponding Author:

Duy-Hung Ha,

Wireless Communications Research Group Faculty of Electrical and Electronics Engineering Ton Duc Thang University, Ho Chi Minh City, Vietnam.

Email: [email protected]

1. INTRODUCTION

Radiofrequency (RF) energy harvesting (EH) in the wireless communication network is become a novel solution for the communication network with battery-limited devices and has attracted massive attention in research and industrial directions. The communication network with the battery-limited devices or devices and wireless sensors, which are working in the dangerous conditions is the main inside human bodies object of RF EH wireless communication network application. This solution can be considered as the main one because of carrying both energy and information of the EF, to help the battery-limited devices to harvest energy for information transmission to the destination. This technic is called simultaneous wireless information and power transfer (SWIPT) [1-11]. Nowadays, the physical layer security (PLS) in EH communication cooperative relaying network is popularly studied with considerable interest. The first concept of PLS was proposed by authors in [12, 13]. In this paper, the author proposed the secret communication between the source and destination nodes with the presence of the eavesdropper channel.

Furthermore, the côperative jammer is used for secure the cooperative relaying network by degrading the eavesdropper’s channel is proposed and studied in [14, 15]. In this cooperative network, the jammer not

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only is used to degrade the eavesdropper’s channel but also is helpful for increasing the EH process of the energy receiver in the cooperative relaying network. Moreover, a harvest-and-jam (HJ) protocol with multi-relay and multi-node in the cooperative relaying network was proposed in [16] to improve the secrecy rate of the energy harvesting and information transmission. Also, different secure relay beam-forming algorithms for SWIPT were discussed in [17-20].

In this research, we proposed and investigated physical security with power beacon assisted in half-duplex relaying networks over a Rayleigh fading channel. In this model, the source (S) node communicates with the destination (D) node via the helping of the intermediate relay (R) node. The D and R nodes harvest energy from the power beacon (PB) node in the presence of a passive Eavesdropper (E) node.

Then we derived the integral form of the system outage probability (OP) and closed form of the intercept probability (IP). The correctness of the analytical of the OP and IP is verified by the Monte Carlo simulation.

The influence of the main system parameters on the OP and IP also is investigated. The research results indicated that the analytical results are the same as the simulation ones.

2. SYSTEM MODEL

In Figure 1, the source (S) node communicates with the destination (D) node via the helping of the intermediate relay (R) node. The D and R nodes harvest energy from the power beacon (PB) node in the presence of a passive Eavesdropper (E) node. Figure 2 draws the energy harvesting (EH) and information processing (IT) of the model system. In this protocol, the transmission is divided into blocks of length T, which consists of three-time slots. In the first time slot αT (α is the time switching factor, 0<α<1), the S and R harvest energy from the PB node. In the remaining intervals time (1-α)T/2, the source S transfers the information to R, and R transfers information to D node [21-25].

Figure 1. System model Figure 2. Time switching protocol

2.1. Energy harvesting phase

In the first phase, the power beacon will supply the energy for both S and R nodes.

Hence, the harvested energy at the source and relay can be given as, respectively

𝐸𝑠= 𝜂𝑃𝐵𝛼𝑇|ℎ𝐵𝑆|² (1)

𝐸_𝑅= 𝜂𝑃_𝐵𝛼𝑇|ℎ𝐵𝑅|² (2)

where 0 < 𝜂 ≤ 1 is energy conversion efficiency, PB is the average transmitted power at the power beacon, and hBS, hBR are the channel gain of B-S link, B-R link, respectively. The average transmitted power at the source and relay nodes can be obtained from (1) and (2), respectively

𝑃_𝑠= ^𝐸^𝑠

(1−𝛼)𝑇/2=^𝜂𝑃^𝐵^𝛼𝑇|ℎ^𝐵𝑆^|²

(1−𝛼)𝑇/2 = 𝜅𝑃_𝐵|ℎ𝐵𝑆|² (3)

𝑃𝑅= 𝜅𝑃𝐵|ℎ𝐵𝑅|² (4)

where =^2𝜂𝛼

1−𝛼 .

2.2. Information transmission phase

In the second phase, the received signal at the relay can be rewritten as

𝑦_𝑟=ℎ_𝑆𝑅𝑥_𝑠+ 𝑛_𝑟 (5)

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where hSR is the channel gain of S-R link, xs is the transmitted signal from source and nr is additive white Gaussian noise (AWGN) with variance N0. In the third phase, the received signal at the destination can be given by

𝑦_𝑑=ℎ𝑅𝐷𝑥_𝑟+ 𝑛_𝑑 (6)

where hRD is the channel gain of R-D link, xr is the transmitted signal from relay and nd is (AWGN) with variance N0. Here, we consider amplify and forward (AF) mode at R. Hence, the amplifying factor can be given as

𝜒 =^𝑥^𝑟

𝑦_𝑟= √_𝑃 ^𝑃^𝑅

𝑠|ℎ𝑆𝑅|²+𝑁₀ (7)

substituting (7) into (6), we have

𝑦_𝑑=ℎ_𝑅𝐷𝜒𝑦_𝑟=ℎ_𝑅𝐷𝜒[ℎ_𝑆𝑅𝑥_𝑠+ 𝑛_𝑟] + 𝑛_𝑑=ℎ⏟ _𝑆𝑅ℎ_𝑅𝐷𝜒𝑥_𝑠

𝑠𝑖𝑔𝑛𝑎𝑙

+ℎ⏟ _𝑅𝐷𝜒𝑛_𝑟+ 𝑛_𝑑

𝑛𝑜𝑖𝑠𝑒

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3. SYSTEM PERFORMANCE ANALYSIS

From (8), the end to end signal to noise ratio (SNR) of S-R-D link can be calculated as (9).

𝛾_𝑆𝑅𝐷=^{𝛦{|𝑠𝑖𝑔𝑛𝑎𝑙|}²^}

𝛦{|𝑛𝑜𝑖𝑠𝑒|²} =^|ℎ^𝑆𝑅^|²^|ℎ^𝑅𝐷^|²^𝜒²^𝑃^𝑠

|ℎ_𝑅𝐷|²𝜒²𝑁₀+𝑁₀ =^|ℎ^𝑆𝑅^|²^|ℎ^𝑅𝐷^|²^𝑃^𝑠

|ℎ_𝑅𝐷|²𝑁₀+^𝑁0 𝜒2

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After doing some algebra and using the fact that N0<<PR, the (9) can be rewritten as (10).

𝛾𝑆𝑅𝐷= ^|ℎ^𝑆𝑅^|²^|ℎ^𝑅𝐷^|²^𝑃^𝑠^𝑃^𝑅

𝑃_𝑅|ℎ𝑅𝐷|²𝑁₀+𝑁₀𝑃_𝑠|ℎ𝑆𝑅|² (10)

Substituting (3) and (4) into (10), the SNR can be reformulated as (11).

𝛾𝑆𝑅𝐷=^|ℎ^𝑆𝑅^|²^|ℎ^𝑅𝐷^|²^𝜅𝛹|ℎ^𝐵𝑆^|²^|ℎ^𝐵𝑅^|²

|ℎ𝐵𝑅|²|ℎ𝑅𝐷|²+|ℎ𝐵𝑆|²|ℎ𝑆𝑅|² =^{𝜅𝛹𝑋𝑌}

𝑋+𝑌 (11)

Where =^𝑃^𝐵

𝑁₀, 𝑋 = |ℎ𝐵𝑅|²|ℎ𝑅𝐷|², 𝑌 = |ℎ𝐵𝑆|²|ℎ𝑆𝑅|² . The received signal at the eavesdropper can be given by

𝑦_𝐸=ℎ𝑅𝐸𝑥_𝑟+ 𝑛_𝐸 (12)

where hRE is the channel gain of R-E link and nE is AWGN with variance N0. The SNR at the eavesdropper can be expressed as

𝛾_𝐸=^|ℎ^𝑅𝐸^|²^𝑃^𝑅

𝑁₀ (13)

substituting (4) into (13), we have:

𝛾_𝐸= 𝜅𝛹|ℎ_𝐵𝑅|²|ℎ_𝑅𝐸|²= 𝜅𝛹𝑍 (14)

Where 𝑍 = |ℎ𝐵𝑅|²|ℎ𝑅𝐸|²

Lemma1. Please note that all channel are the Rayleigh fading channels, so the probability density function (PDF) of |ℎ𝑖|² can be given by:

𝑓_|ℎ_𝑖_|²(𝑥) = 𝜆𝑖𝑒^−𝜆^𝑖^𝑥 (15)

where 𝑖 ∈ (𝑆𝑅, 𝑅𝐷, 𝐵𝑆, 𝐵𝑅, 𝑅𝐸). Moreover, the cumulative distribution function (CDF) of |ℎ𝑖|² also can be obtained by

𝐹_|ℎ_𝑖_|²(𝑥) = 1 − 𝑒^−𝜆^𝑖^𝑥 (16)

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where𝜆𝑖is the mean value of the exponential random variable |ℎ𝑖|². Lemma 2. The CDF of 𝑋and Y can be computed as respectively

𝐹_𝑋(𝑎) = ∫ 𝐹_|ℎ_𝑅𝐷|²( ^𝑎

|ℎ𝐵𝑅|²||ℎ_𝐵𝑅|²= 𝑥) 𝑓_|ℎ_𝐵𝑅_|2(𝑥)𝑑𝑥

∞

0 (17)

𝐹_𝑌(𝑏) = ∫ 𝐹|ℎ𝑆𝑅|²( ^𝑏

|ℎ_𝐵𝑆|²||ℎ𝐵𝑆|²= 𝑦) 𝑓_|_ℎ_𝐵𝑆_|2(𝑦)𝑑𝑦

∞

0 (18)

utilizing the result in [26], the CDF of X and Y can be shown as the below equation, respectively 𝐹_𝑋(𝑎) = 1 − 2√𝜆_𝑅𝐷𝜆_𝐵𝑅𝑎𝐾₁(2√𝜆_𝑅𝐷𝜆_𝐵𝑅𝑎) (19) 𝐹𝑌(𝑏) = 1 − 2√𝜆𝑆𝑅𝜆𝐵𝑆𝑏𝐾1(2√𝜆𝑆𝑅𝜆𝐵𝑆𝑏) (20) where 𝐾𝑣(•)is the modified Bessel function of the second kind and v^th order. From (21) and (22), the PDF of X and Y can be calculated as, respectively after applying the formula

𝜕𝐾_𝑛(𝑧)

𝜕𝑧 = −𝐾𝑛−1(𝑧) −^𝑛

𝑧𝐾𝑛(𝑧) 𝑓𝑋(𝑎) =^𝜕𝐹^𝑋^(𝑎)

𝜕𝑎 = 2√𝜆𝑅𝐷𝜆𝐵𝑅𝐾0(2√𝜆𝑅𝐷𝜆𝐵𝑅𝑎) (21)

𝑓𝑌(𝑏) =^𝜕𝐹^𝑋^(𝑏)

𝜕𝑏 = 2√𝜆𝑆𝑅𝜆𝐵𝑆𝐾0(2√𝜆𝑆𝑅𝜆𝐵𝑆𝑏) (22)

3.1. Outage probability (OP)

The OP of system can be given as

𝑂𝑃 = 𝑃𝑟(𝛾_𝑆𝑅𝐷< 𝛾_𝑡ℎ) (23)

where 𝛾_𝑡ℎ= 2^2𝑅− 1 is the threshold of system and R is source rate. Substituting (11) into (23), we have 𝑂𝑃 = 𝑃𝑟 (^{𝜅𝛹𝑋𝑌}

𝑋+𝑌 < 𝛾_𝑡ℎ) = 𝑃𝑟(𝑋[𝜅𝛹𝑌 − 𝛾_𝑡ℎ] < 𝛾_𝑡ℎ𝑌)

= {𝑃𝑟 (𝑋 < ^𝛾^𝑡ℎ^𝑌

𝜅𝛹𝑌−𝛾_𝑡ℎ) , 𝑌 >^𝛾^𝑡ℎ

𝜅𝛹

1, 𝑌 ≤^𝛾^𝑡ℎ

𝜅𝛹

= ∫₀^𝛾𝑡ℎ^𝜅𝛹𝑓𝑌(𝑦)𝑑𝑦+ ∫ 𝐹𝑋 𝛾𝑡ℎ∞ 𝜅𝛹

( ^𝛾^𝑡ℎ^𝑌

𝜅𝛹𝑌−𝛾_𝑡ℎ|𝑌 = 𝑦) × 𝑓𝑌(𝑦)𝑑𝑦 (24)

Applying (19-22), (24) can be rewritten as (25).

𝑂𝑃 = ∫ 2√𝜆₀^∞ _𝑆𝑅𝜆_𝐵𝑆𝐾₀(2√𝜆_𝑆𝑅𝜆_𝐵𝑆𝑦)𝑑𝑦− 4 ∫

√𝜆_𝑆𝑅𝜆_𝐵𝑆𝜆_𝑅𝐷𝜆_𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦

𝜅𝛹𝑦−𝛾𝑡ℎ] ×

𝐾₀(2√𝜆_𝑆𝑅𝜆_𝐵𝑆𝑦)𝐾₁(2√𝜆_𝑅𝐷𝜆_𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦

𝜅𝛹𝑦−𝛾𝑡ℎ]) 𝑑𝑦

𝛾𝑡ℎ∞ 𝜅𝛹

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By changing the variable for the first term of (25): 𝑡 = 2√𝜆𝑆𝑅𝜆_𝐵𝑆𝑦.

𝑂𝑃 = ¹

√𝜆_𝑆𝑅𝜆_𝐵𝑆∫ 𝑡 × 𝐾^∞ 0(𝑡)𝑑𝑡

0 − 4 ∫

√𝜆𝑆𝑅𝜆𝐵𝑆𝜆𝑅𝐷𝜆𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦

𝜅𝛹𝑦−𝛾_𝑡ℎ] ×

𝐾₀(2√𝜆𝑆𝑅𝜆_𝐵𝑆𝑦)𝐾₁(2√𝜆𝑅𝐷𝜆_𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦

𝜅𝛹𝑦−𝛾_𝑡ℎ]) 𝑑𝑦

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Apply (6.561, 16) of the table of integral, (26) can be reformulated as

𝑂𝑃 = ¹

√𝜆𝑆𝑅𝜆𝐵𝑆− 4 ∫

√𝜆_𝑆𝑅𝜆_𝐵𝑆𝜆_𝑅𝐷𝜆_𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦

𝜅𝛹𝑦−𝛾_𝑡ℎ] ×

𝐾₀(2√𝜆𝑆𝑅𝜆_𝐵𝑆𝑦)𝐾₁(2√𝜆𝑅𝐷𝜆_𝐵𝑅[ ^𝛾^𝑡ℎ^𝑦 ]) 𝑑𝑦

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3.2. Intercept probability (IP) The IP can be defined by

𝐼𝑃 = 𝑃𝑟(𝛾_𝐸≥ 𝛾_𝑡ℎ) (28)

substituting (14) into (28) and then applying formulas in (19) or (20), finally we have:

𝐼𝑃 = 𝑃𝑟(𝜅𝛹𝑍 ≥ 𝛾_𝑡ℎ) = 1 − 𝑃𝑟 (𝑍 <^𝛾^𝑡ℎ

𝜅𝛹) = 2√^𝜆^𝐵𝑅^𝜆^𝑅𝐸^𝛾^𝑡ℎ

𝜅𝛹 × 𝐾₁(2√^𝜆^𝐵𝑅^𝜆^𝑅𝐸^𝛾^𝑡ℎ

𝜅𝛹 ) (29)

4. NUMERICAL RESULTS AND DISCUSSION

The influence of η on the OP and IP is plotted in Figure 3 and Figure 4 for various values of ψ. Here we set α = 0.5, R = 0.5 bps/Hz and ψ = 1, 5, 10 dB. The first observation one can see from these results is that the analytical match very well with the simulation results. Figure 5 and Figure 6 illustrated the optimal switching time system OP and IP versus ψ for η = 0.8, R=0.5 bps/Hz, and α = 0.25, 0.5, 0.85 respectively.

It should be pointed out that the simulation and analytical results are the same.

Figure 3. IP versus η

Figure 4. OP versus η

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Figure 5. IP versus ψ

Figure 6. OP versus ψ

5. CONCLUSION

In this research, we proposed and investigated physical security with power beacon assisted in half- duplex relaying networks over a Rayleigh fading channel. In this model, the source (S) node communicates with the destination (D) node via the helping of the intermediate relay (R) node. The D and R nodes harvest energy from the power beacon (PB) node in the presence of a passive Eavesdropper (E) node. Then we derived the integral form of the system outage probability (OP) and closed form of the intercept probability (IP). The correctness of the analytical of the OP and IP is verified by the Monte Carlo simulation.

The influence of the main system parameters on the OP and IP also is investigated. The research results indicated that the analytical results are the same as the simulation ones.

ACKNOWLEDGMENTS

This research was supported by National Key Laboratory of Digital Control and System Engineering (DCSELAB), HCMUT, VNU-HCM, Vietnam.

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